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Entropy solutions for nonlinear degenerate problems

Carrillo Menéndez, José (1999) Entropy solutions for nonlinear degenerate problems. Archive for rational mechanics and analysis, 147 (4). pp. 269-361. ISSN 0003-9527

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Abstract

We consider a class of elliptic-hyperbolic degenerate equations g(u) - Delta b(u) + div phi (u) = f with Dirichlet homogeneous boundary conditions and a class of elliptic-parabolic-hyperbolic degenerate equations g(u)(t) - Delta b(u) + div phi (u) = f with homogeneous Dirichlet conditions and initial conditions. Existence of entropy solutions for both problems is proved for nondecreasing continuous functions g and b vanishing at zero and for a continuous vectorial function phi satisfying rather general conditions. Comparison and uniqueness of entropy solutions are proved for g and b continuous and nondecreasing and for phi continuous.

Item Type:Article
Uncontrolled Keywords:Parabolic equations; uniqueness
Subjects:Sciences > Mathematics > Differential equations
ID Code:15594
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